Question: Simplify the following expression: $y = \dfrac{1}{10q} - \dfrac{3}{5q}$
Answer: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $10q$ and $5q$ $\lcm(10q, 5q) = 10q$ $ y = \dfrac{1}{1} \cdot \dfrac{1}{10q} - \dfrac{2}{2} \cdot \dfrac{3}{5q} $ $y = \dfrac{1}{10q} - \dfrac{6}{10q}$ $y = \dfrac{1 -6}{10q}$ $y = \dfrac{-5}{10q}$ Simplify the expression by dividing the numerator and denominator by 5: $y = \dfrac{-1}{2q}$